Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2024MathematicsBinomial TheoremActual

Paragraph: Let (8+3 7 )²⁰= U + V and (8-3 7 )²⁰= W , where U is an integer and 0 Question: What is V + W equal to?

Options

  1. A8
  2. B4
  3. C2
  4. D1

Correct answer

D. 1

Step-by-step solution

We have, (8+3 7 )²⁰= U + V ....(i) and (8-3 7 )²⁰= W ....(ii) Here, o < W < 1 Now, adding equation (i) & (ii), we have, aligned & U + V + W =(8+3 7 )²⁰+(8-3 7 )²⁰ & =2 [ ²⁰ C ₀ 8²⁰+ ²⁰ C ₂ 8¹⁸ (3 7 )^2+ .+(3 7 )²⁰ ] aligned R.H.S. is an even number. Also, o < V < 1, o < W < 1 and U is an integer V + W is an integer V + W =1 So, V+W=1

Practice Binomial Theorem on Quantrex Academy →

More from Binomial Theorem

A set S contains (2n+1) elements. If the number of subsets of S which contain at most n elements is 1024 , then what is the value of n ? 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: Consider the following statements : I. (u+v 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of u ? 2026What is the greatest value of r satisfying the inequality 15 r+1 >2 ¹⁵C_r ? 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of uv ? 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of (v+f) ? 2026Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the multiplicative inverse of ( 2 + 2026If the sum of binomial coefficients in the expansion of (x + y)^n is 256, then the greatest binomial coefficient occurs in which one of the following terms? 2025 Full Binomial Theorem list All NDA PYQs